Real-valued functions of a real variable which are continuous with respect to the density topology on both the domain and the range are called density continuous. A typical continuous function is nowhere density continuous. The same is true of a typical homeomorphism of the real line. A subset of the real line is the set of points of discontinuity of a density continuous function if and only if...

This paper presents some important classes of the continuous functions defined from set real numbers to space complex intervals. These function spaces have an algebraic structure named as a quasilinear which is suggested by Aseev in 1986. In this work, we analysis on and interval-valued functions. Further, show that these are normed Ω-spaces. Finally, examine dimension spaces.

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...